Mostly this chapter seemed to be some odds and ends, or tips and tricks for rooks on the 7th rank. The five special cases seemed kind of weird and random, though they weren't uninteresting. It was only with the 5th case that he seemed to have some ideas of a more general nature.
I think the thing to remember here is that Part 1 is called "The Elements" and really he's just introducing the basic ideas. So that may explain some of the piecemeal and less revolutionary seeming aspect to the ideas.
I guess the two main ideas that stuck with me were
1) The 7th rank "absolute"-- this is what he calls it when the rook is on the 7th rank, the opp. king is on the 8th (his own first) and there are no pawns on the 7th. Plus the attacker should have a far advanced passed pawn. He shows the ideas for winning with this situation.
2) The other was the notion of "outflanking"--this is where you have rooks on 7th and opp king on 8th. Then there are various tricks you can try to gain from the situation. Again these were a little hodgepodge but I can see that this would be situation where I might be frustrated feeling that I should be able to get something but not seeing anything, and now I have some more ideas.